The present invention relates to a quadrature amplitude modulation (QAM) type demodulator for demodulating signals modulated in accordance with the QAM scheme.
Quadrature amplitude modulation (QAM) is an intermediate frequency (IF) modulation scheme in which a QAM signal is produced by amplitude modulating two baseband signals, generated independently of each other, with two quadrature carriers, respectively, and adding the resulting signals. The QAM modulation is used to modulate a digital information into a convenient frequency band. This may be to match the spectral band occupied by a signal to the passband of a transmission line, to allow frequency division multiplexing of signals, or to enable signals to be radiated by smaller antennas. QAM has been adopted by the Digital Video Broadcasting (DVB) and Digital Audio Visual Council (DAVIC) and the Multimedia Cable Network System (MCNS) standardization bodies for the transmission of digital TV signals over Coaxial, Hybrid Fiber Coaxial (HFC), and Microwave Multi-port Distribution Wireless Systems (MMDS) TV networks.
The QAM modulation scheme exists with a variable number of levels (4, 16, 32, 64, 128, 256, 512, 1024) which provide 2, 4, 5, 6, 7, 8, 9, and 10 Mbit/s/MHz. This offers up to about 42 Mbit/s (QAM-256) over an American 6 MHz CATV channel, and 56 Mbit/s over an 8 MHz European CATV channel. This represents the equivalent of 10 PAL or SECAM TV channels transmitted over the equivalent bandwidth of a single analog TV program, and approximately 2 to 3 High Definition Television (HDTV) programs. Audio and video streams are digitally encoded and mapped into MPEG2 transport stream packets, consisting of 188 bytes.
The bit stream is decomposed into n bits packets. Each packet is mapped into a QAM symbol represented by two components I and Q, (e.g., n=4 bits are mapped into one 16-QAM symbol, n=8 bits are mapped into one 256-QAM symbol). The I and Q components are filtered and modulated using a sine and a cosine wave (carrier) leading to a unique Radio Frequency (RF) spectrum. The I and Q components are.usually represented as a constellation which represents the possible discrete values taken over in-phase and quadrature coordinates. The transmitted signal s(t) is given by:
s(t)=I cos(2xcfx80f0t)xe2x88x92Q sin(2xcfx80f0t),
where f0 is the center frequency of the RF signal. I and Q components are usually filtered waveforms using raised cosine filtering at the transmitter and the receiver. Thus, the resulting RF spectrum is centered around f0 and has a bandwidth of R(1+xcex1), where R is the symbol transmission rate and xcex1 is the roll-off factor of the raised cosine filter. The symbol transmission rate is 1/nth of the transmission bit rate, since n bits are mapped to one QAM symbol per time unit 1/R.
In order to recover the baseband signals from the modulated carrier, a demodulator is used at the receiving end of the transmission line. The receiver must control the gain of the input amplifier that receives the signal, recover the symbol frequency of the signal, and recover the carrier frequency of the RF signal. After these main functions, a point is received in the I/Q constellation which is the sum of the transmitted QAM symbol and noise that was added over the transmission. The receiver then carries out a threshold decision based on lines situated at half the distance between QAM symbols in order to decide on the most probable sent QAM symbol. From this symbol, the bits are unmapped using the same mapping as in the modulator. Usually, the bits then go through a forward error decoder which corrects possible erroneous decisions on the actual transmitted QAM symbol. The forward error decoder usually contains a de-interleaver whose role is to spread out errors that could have happened in bursts and would have otherwise have been more difficult to correct.
Generally, in a data receiver, the timing must be synchronized to the symbols of the incoming data signal. In analog-implemented systems, synchronization is typically performed by altering the phase of a local clock or by regenerating a timing wave from the incoming signal. However, in circumstances involving digital techniques, wherein the signal is sampled, the sampling clock must remain independent of the symbol timing. In these circumstances, interpolation filtering is used to process the digital samples produced by an analog-to-digital converter.
Two related articles by F.M. Gardner [(1) F. M. Gardner, xe2x80x9cInterpolation in Digital Modemsxe2x80x94Part I: Fundamentalsxe2x80x9d, IEEE Transactions on Communications, Vol. 41, No. 3, March 1993, and (2) F. M. Gardner, xe2x80x9cInterpolation in Digital Modemsxe2x80x94Part II: Implementation and Performancexe2x80x9d, IEEE Transactions on Communications, Vol. 41, No. 6, June 1993] describe a fundamental equation for interpolation. In the articles, Gardner proposes a method for interpolation control, outlines the signal-processing characteristics appropriate to an interpolator and describes implementation of the interpolation control method. As will be described in more detail in the description of the present invention, the mathematical model for interpolation with a time-continuous filter includes a fictitious digital-to-analog converter, followed by a time-continuous filter h(t), and a resampler at time t=kTi. The output interpolants are represented by                               y          ⁡                      (                          kT              i                        )                          =                              ∑            m                    ⁢                      xe2x80x83                    ⁢                                    x              ⁡                              (                                  mT                  s                                )                                      ⁢                          h              ⁡                              (                                                      kT                    i                                    -                                      mT                    s                                                  )                                                                        (        A        )            
The value mTs represents the instants of sampling of the analog-to-digital converter. The resample-instants t=kTi are delivered by numerically controlled oscillator. The numerically controlled oscillator produces two signals at each time mTs. The first signal is an overflow signal xcex6, which indicates that a resample instant (t=kTi) has occurred during the last Ts period. The second signal is a Tixe2x80x94fractional signal xcex7, such that xcex7Ti represents the time since the last resample instant.
In the interpolation method proposed in the Gardner references, equation (A) is rearranged by introducing a fractional interval,       μ    ⁢          xe2x80x83        ⁢    k    =                    kT        i                    T        s              -          m      k      
and a filter index   i  =            int      ⁢              xe2x80x83            [                        kT          i                          T          s                    ]        -    m  
Equation (A) can then be rewritten as                               y          ⁡                      (                          kT              i                        )                          =                              ∑                          i              =                              I                1                                                                    I                2                            -              1                                ⁢                      xe2x80x83                    ⁢                                    x              ⁡                              [                                                      (                                          mk                      -                      i                                        )                                    ⁢                                      T                    s                                                  ]                                      ⁢                          h              ⁡                              [                                                      (                                          i                      +                                              μ                        ⁢                                                  xe2x80x83                                                ⁢                        k                                                              )                                    ⁢                                      T                    s                                                  ]                                                                        (        B        )            
Then, a finite impulse response of length (I2xe2x88x92I1+1) Ts was chosen for h(t). With this choice, Equation (A) can be computed with a finite impulse response filter with (I2xe2x88x92I1+1) taps. Each of these taps is computed as a function of fractional interval xcexck, which provides the result:
h((i+xcexck)Ts)=fi(xcexck)xe2x80x83xe2x80x83(C)
As a consequence, the impulse response h(t) is a function of the variable t/Ts. This means that the filtering properties of the interpolator, such as the bandwidth for example, are fixed with respect to the sampling clock, and are not dependent on the useful part of the input signal x(t). Generally, for an ideal input signal x(t), the interpolated signal, y, is more attenuated for a high baud rate 1/T because then the bandwidth of the input signal is larger with respect to the interpolator bandwidth. In addition, in practical modem applications, the input signal x(t) is the sum of the useful signal xu(t), with bandwidth proportional to the transmission rate 1/T, and the residual impairment signal Xm, which has to be filtered and which may have a bandwidth as large as 1/Ts. In this case, it is evident that the interpolated impairment signal Ym is much more important in cases where there is a low transmission rate 1/T, than in cases where there is a high transmission rate.
In the prior art interpolation methods, such as that described in the Gardner references, the fractional interval index is not directly output by the numerically controlled oscillator and therefore has to be computed. The Gardner reference proposes an exact formula for xcexck:                               μ          ⁢                      xe2x80x83                    ⁢          k                =                              η            ⁢                          xe2x80x83                        ⁢                          (                              m                k                            )                                            W            ⁡                          (                              m                k                            )                                                          (        D        )            
and also proposes some practical approximations to implement this division. Additionally, in practical implementation with Digital Signal processors or other circuits, the computation power is not efficiently used for low transmission rates, 1/T. Therefore, as the transmission rate decreases, the processor activity and filtering performance also decreases.
It is the object of the present invention to provide a timing recovery circuit in a QAM demodulator that uses an interpolation method that is independent of the symbol rate and that rejects most of the signal outside the bandwidth of the receive channel.
It is a further object of the invention to provide a timing recovery circuit that uses an interpolation method that allows the timing and frequency response of the interpolation to be invariant with respect to the interpolants rate, and thus with respect to the transmission rate.
The above objects have been achieved by a timing recovery circuit in a QAM demodulator which uses a symbol rate continuously adaptive interpolation filter. As opposed to prior art methods of interpolation which use interpolation functions which are defined as a function of t/Ts (time/sampling interval), the method of interpolation used in the present invention is defined as a function of t/Ti (time/interpolation interval). This allows the interpolation filtering to be totally independent of the symbol rate in terms of complexity and performance and provides a better rejection of adjacent channels, since the interpolator rejects most of the signal outside the bandwidth of the received channel.
The resampled signal is delivered to the interpolation filter by a numerically controlled oscillator which is controlled by a signal which estimates the ratio of sampling interval/interpolation interval. The interpolants are practically implemented by using a multiplicator-accumulator operator. The output of the timing recovery circuit is supplied to a receive filter and then to a carrier recovery circuit to recover the carrier signal.